WASHINGTON  Republicans and Democrats alike on Sunday predicted President Barack Obama would fail if he pushed forward with his own effort to overhaul the nation’s immigration system and urged the administration to hold off while lawmakers work on a bipartisan measure.

Republican Sen. John McCain predicted the administration’s efforts would come up short if the White House went forward with a proposal to put the estimated 11 million illegal immigrants in the U.S. on a long pathway to citizenship. Democratic Sen. Chuck Schumer, who met with Obama on Wednesday at the White House to discuss progress, urged his allies in the administration to give a bipartisan group of eight lawmakers the time to hammer out a deal on their own.

Obama’s newly appointed top aide, chief of staff Denis McDonough, said the White House would only send its plan to Congress if the lawmakers stumble in their efforts and cast its efforts as a back-up plan.

“Well, let’s make sure that it doesn’t have to be proposed,” McDonough said of the president’s pitch, first reported on USA Today’s website late Saturday.

“We will be prepared with our own plan if these ongoing talks between Republicans and Democrats up on Capitol Hill break down,” McDonough said in a second interview, adding he’s optimistic they would not crumble.

The administration’s proposal would create a visa for those in the country illegally and allow them to become legal permanent residents within eight years. The proposal also requires businesses to know the immigration status of their workers and adds more funding for border security.

It drew immediate criticism from Sen. Marco Rubio, R-Fla.

“If actually proposed, the president’s bill would be dead on arrival in Congress, leaving us with unsecured borders and a broken legal immigration system for years to come,” said Rubio, who is among the eight lawmakers searching for a comprehensive plan.

Many of the details in the administration’s draft proposal follow the broad principles that Obama previously outlined. But the fact the administration is writing its own alternative signaled Obama wants to address immigration sooner rather than later and perhaps was looking to nudge lawmakers to move more quickly.